This invention pertains generally to quantum computers, and in particular to a solid state quantum computer comprising a crystal lattice.
A quantum computer is a machine that prepares a quantum mechanical system in an initial input state, performs unitary logic operations on the system, and measures a resulting output state. The superposition principle of quantum mechanics and the quantum interference induced by a projective measurement bring about xe2x80x9cquantum parallelism,xe2x80x9d by which certain problems can be computed faster than by any classical computer.
Several physical systems are known to provide the quantum mechanical states that carry quantum bit, or xe2x80x9cqubit,xe2x80x9d information. Each of these systems carries its own disadvantages. (i) Cold trapped ions, cavity quantum electrodynamics, and combinations of the two systems allow computation and final readout to be performed on individual qubits. However, these techniques require immense experimental exertion. (ii) Single photon gates, compatible with quantum communication links, are possible only in the presence of large optical nonlinearity with negligible loss. (iii) Systems of nuclear spins in solution molecules are based on natural and simple chemical structures and well-established techniques of pulsed nuclear magnetic resonance. However, such systems demand a large number of molecules to detect the output signals from slight population differences between nuclei with up spins and those with down spins. Furthermore, these liquid systems cannot be cooled to low temperatures to reduce thermal noise, since the liquids would freeze. (iv) Solid state systems can be used, including quantum dots, Josephson junctions, and nuclear spins of implanted phosphorous ions in silicon. However, these solid state systems would require technical breakthroughs before they could be scaled up to large numbers of distinct qubits.
There is a need, therefore, for a quantum computer that does not require cumbersome experimental techniques, that can be cooled to low temperatures, and that can be scaled to large numbers of qubits.
A solid state crystal can be considered for quantum computation, wherein qubits are represented by spins of individual atoms or nuclei. However, it is not obvious how to distinguish between adjacent spins in the crystal, since the spins are so close together (on the order of 10 angstroms). Furthermore, spurious couplings among the atoms of the crystal will contaminate the quantum computation.
It is therefore a primary object of the present invention to provide a crystal lattice quantum computer wherein quantum bits are represented by nuclear spins, and adjacent spins can be distinguished. It is a further object of the present invention to cancel the spurious couplings within the crystal to reduce the error rate of the quantum computer.
The quantum computer of the present invention has the advantages that it has a relatively simple design, it can be cooled to low temperatures, and can be scaled up to include a large number of quantum bits.
Furthermore, the nuclear spins that store the quantum bits have a long relaxation time and are isolated from their surrounding environment. The nuclei are regularly spaced in the crystal lattice, allowing them to be precisely addressed. The nuclei have spin-1/2, and have no isotopes with different nuclear spins. Finally, the nuclei are surrounded by localized electrons, allowing a magnetic order of the electrons to be utilized to initialize the nuclear spins efficiently.
A quantum computer comprises a crystal lattice having storage atoms. The storage atoms have nuclear storage spins. Quantum bits are stored as orientations of the storage spins. A magnetic field is applied to the crystal, the magnetic field having a gradient strong enough to cause energy levels of adjacent storage atoms along the direction of the gradient to be significantly different. The gradient is preferably created by a micromagnet in the vicinity of the crystal. The micromagnet preferably has a width on the order of 1 xcexcm or less and generates a gradient on the order of 1 xcexcm. The micromagnet preferably comprises dysprosium.
The electrons of the crystal acquire a regular order. This order is utilized to initialize the storage spins as follows: combined electron-nucleus transitions are induced in the crystal, resulting in the transfer of the electronic order to the polarizations of the storage spins.
The storage spins are decoupled from each other by applying a time-varying decoupling magnetic field. The decoupling field eliminates spurious couplings that otherwise plague the crystal. The decoupling field rotates the storage spins in such a way as to cancel their magnetic dipole-dipole interactions. The decoupling field preferably comprises series of xcfx80/2-pulses.
Quantum logic operations are performed on the storage spins. In a one-bit gate, a storage spin is rotated by an angle xcex8. A two-bit exclusive-OR gate involves the interaction of two storage spins. To carry out the exclusive-OR operation, the two storage spins must be recoupled by either modifying or switching off the decoupling field. The exclusive-OR operation is then achieved by applying an oscillating magnetic field to the crystal, wherein the oscillating magnetic field has a frequency equal to a resonance frequency of the recoupled storage spins.
Measurement of final polarizations of the storage spins is achieved by applying an oscillating measurement magnetic field to the crystal and measuring an amount of absorption of the measurement field. In the preferred embodiment, the crystal comprises measurement atoms, and the measurement field has a frequency equal to a resonant frequency of a coupled system comprising at least one measurement atom and at least one storage atom.